We propose a lattice version of Chern-Simons gravity and show that the partition function coincides with Ponzano-Regge model and the action leads to the Chern-Simons gravity in the continuum limit. The action is explicitly constructed by lattice dreibein and spin connection and is shown to be invariant under lattice local Lorentz transformation and gauge diffeomorphism. The action includes the ...

Transformation properties of Dirac equation correspond to Spin(3,1) representation of Lorentz group SO(3,1), but group GL(4,R) of general relativity does not accept a similar construction with Dirac spinors. On the other hand, it is possible to look for representation of GL(4,R) in some bigger space, there Dirac spinors are formally situated as some " subsystem. " In the paper is described cons...

Transformation properties of Dirac equation correspond to Spin(3,1) representation of Lorentz group SO(3,1), but group GL(4,R) of general relativity does not accept spinor representation. On the other hand, it is possible to look for representation of GL(4,R) in some bigger space, there Dirac spinors are formally situated as some " subsystem. " In the paper is described construction of such rep...

Acceleration-induced nonlocality and the corresponding Lorentz-invariant nonlocal field equations of accelerated systems in Minkowski spacetime are discussed. Under physically reasonable conditions, the nonlocal equation of motion of the field can be derived from a varia-tional principle of stationary action involving a nonlocal Lagrangian that is simply obtained by composing the local inertial...

The relativistic generalization of the Brownian motion is discussed. We show that the transformation property of the noise term is determined by requiring for the equilibrium distribution function to be Lorentz invariant, such as the Jüttner distribution function. It is shown that this requirement generates an entanglement between the force term and the noise so that the noise itself should not...

It is then easy to derive the well-known Lorentz transformation equations, those equations which allow us to convert between events measured in one frame to those measured in the other. Two observers in different frames may not measure the same events at the same place or time, but they must agree on all of the laws of physics regarding those events in order for the principle of relativity to h...

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Transformation properties of Dirac equation correspond to Spin(3,1) representation of Lorentz group SO(3,1), but group GL(4,R) of general relativity does not accept spinor representation. On the other hand, it is possible to look for representation of GL(4,R) in some bigger space, there Dirac spinors are formally situated as some " subsystem. " In the paper is described construction of such rep...

A new derivation of the relativistic aberration formula for a plane-polarized light wave is presented that does not require any use of the Lorentz transformation. The method is based on a modification of the Huygens-Fresnel principle to include the relativistic effects introduced by the relative motion between the observer and the emitter. The derivation clearly shows that the aberration formul...

In relativistic heavy ion collisions an exact multipole decomposition of the Lorentz transformed time dependent Coulomb potentials in a coordinate system with equal constant, but opposite velocities of the ions, is obtained for both zero and different from zero impact parameter. The case of large values of γ and the gauge transformation of the interaction removing both the γ dependence and the ...